Matematical Modelling in Biology and Medicine WM-MA-Z-S1-E5-Mmwbim
The aim of the course is to introduce the basics of classical mathematical modeling in biology, epidemiology and medicine. In particular, the student will learn biological and medical applications of integrals and derivatives; equations and systems of ordinary differential equations modeling the development of populations, epidemics, and diseases; discrete models in genetics based on Markov chains. The student will also acquire basic skills in understanding models, their construction, their application in practice and their mathematical analysis.
(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się
(in Polish) E-Learning
Term 2023/24_Z: (in Polish) E-Learning | Term 2024/25_Z: (in Polish) E-Learning | Term 2022/23_Z: (in Polish) E-Learning (pełny kurs) z podziałem na grupy |
(in Polish) Grupa przedmiotów ogólnouczenianych
(in Polish) Opis nakładu pracy studenta w ECTS
Term 2023/24_Z: LECTURE
participation in classes - 20 h
consultations - 6 h
exam - 4 hours
independent reading - 10 h
preparation for the exam - 10 hours
total 50 hours, i.e. 2 ECTS
EXERCISES
participation in classes - 20 h
preparation of papers - 15 hours
housework - 15 h
total 50 hours, i.e. 2 ECTS | Term 2024/25_Z: LECTURE
participation in classes - 20 h
consultations - 6 h
exam - 4 hours
independent reading - 10 h
preparation for the exam - 10 hours
total 50 hours, i.e. 2 ECTS
EXERCISES
participation in classes - 20 h
preparation of papers - 15 hours
housework - 15 h
total 50 hours, i.e. 2 ECTS | Term 2022/23_Z: (in Polish) WYKŁAD
uczestnictwo w zajęciach - 20 h
konsultacje - 6 h
egzamin - 4 h
samodzielna lektura - 10 h
przygotowanie do egzaminu - 10 h
razem 50 h czyli 2 ECTS
ĆWICZENIA
uczestnictwo w zajęciach - 20 h
przygotowanie referatów - 15 h
prace domowe - 15 h
razem 50 h czyli 2 ECTS |
Subject level
Learning outcome code/codes
Type of subject
Preliminary Requirements
Course coordinators
Term 2023/24_Z: | Term 2024/25_Z: | Term 2022/23_Z: |
Learning outcomes
The student knows and understands: (MA1_W01, MA1_W03)
W1.1 - using the derivative as the rate of change or gradient of a given quantity,
W1.2 - construction, applications and limitations of polynomial regression;
W2 - differential equation (dimension 1 or higher) which is a biological and epidemiological model, the concept of steady states, their stability and their importance in models; including models: exponential and logistic, L-V, SIR, their variants; other models;
W3 - basic discrete models which are numerical schemes for solving RRZ and discrete models based on Markov chains.
The student is able to (MA_W03, MA1_U01)
U1 - solve problems requiring the use of derivatives, integrals, research on the course of function variability in biological and epidemiological applications,
U2 - perform basic analysis of the RRZ-based model, its steady states, stability, interpret mathematical conclusions in a real context;
U3 - carry out basic analysis of a model based on a Markov-type process, its absorbing states, expected value;
The student is ready: (MA1_K01, MA1_K02)
K1 - prepare a paper presenting a new issue,
K2 - participate in a scientific discussion.
Assessment criteria
Assessment on the basis of papers presented on the subject of the subject, db, bdb - test.
For all effects, the following assessment criteria are adopted for all forms of verification:
grade 5: fully achieved (no obvious shortcomings)
grade 4.5: achieved almost fully and criteria for awarding a higher grade are not met
grade 4: largely achieved and the criteria for a higher grade are not met
grade 3.5: largely achieved - with a clear majority of positives - and the criteria for granting a higher grade are not met
grade 3: achieved for most of the cases covered by the verification and criteria for a higher grade are not met
grade 2: not achieved for most of the cases covered by the verification
Bibliography
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Term 2023/24_Z:
Required literature Additional literature |
Term 2024/25_Z:
Required literature Additional literature |
Notes
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Term 2023/24_Z:
3rd year. nst. |
Term 2024/25_Z:
3rd year. nst. |
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: